Fast joint estimation of direction of arrival and towed array shape based on marginal likelihood maximization

This paper addresses the joint estimation problem of directions of arrival of sources and towed array shape. Ocean currents and the maneuvering of the towing platform often cause the towed array to bend rather than stay in a straight line, so the array shape must be estimated to avoid performance degradation due to array mismatch. Existing joint estimation methods suffer from high computational complexity or the need for external sensors installed on the array. Therefore, this paper proposes a fast joint estimation algorithm that solely utilizes received acoustic data. The joint estimation is transformed into a sparse reconstruction optimization problem within the Bayesian estimation framework. Firstly, by decomposing the marginal likelihood function, a closed-form solution for the signal variance in the spatial domain is obtained. Then, the towed array shape is introduced as a hyperparameter into the marginal likelihood function and optimized using the quasi-Newton method. In this way, we accomplish joint estimation and reduce computational complexity. Multi-source simulation results show that the proposed method achieves high resolution and fast computational speed. The robustness and efficiency of the proposed joint estimation method are demonstrated by experimental results in the South China Sea.